Data Acquisition

adjustable in a range ± n LSB. This means that where the input range to a 12-bit A/Dconverter is 0–10 V, and the input is set to +1/2 LSB (i.e. +1.22 mV), the digital outputwould read no greater than 0 × 005h. This would represent a maximum offset voltageadjustment of 5/4096 × 10 V = 12.2 mV. Where the input range to a 12-bit A/D converter is0–10 V, and the input is set to –3/2 LSB (i.e. +9.996 V), the digital output would read no lessthan 0 × 99 Ah. For gain accuracy, this figure represents the maximum gain error.Autocalibration, where the entire analog section of the board (multiplexer, amplifier,sample and hold), as well as the A/D converter, is automatically calibrated without userintervention, is provided on some A/D boards.Several auto-calibration methods are used:• Calibration is carried out automatically when a voltage reference is connected tothe board.• Calibration takes place as part of the conversion process.• The accuracy on each input channel is checked for all available gain settings. Acorrection code for each channel/gain combination is stored, then recalled todynamically compensate for drift in hardware.One of the most critical factors confronting users of data acquisition systems and A/D boardsis the question of how frequently should an analog signal be sampled to be able to representand reconstruct the input signal accurately. How fast should the A/D board be able to samplethe data?5.5.1 Nyquist’s theorem5.5.2 AliasingNyquist’s sampling theorem states that:An analog band-limited signal that has no spectral components at or above a frequency ofF Hz can be uniquely represented by samples of its values spaced at uniform intervals thatare no more than 1/2 F seconds apart or sampled at a frequency of no less than 2 F Hz.The maximum sampling period, T=l/2 F, is known as the Nyquist interval, while theminimum sampling frequency, corresponding to this period, 2 F, is known as the Nyquistsampling frequency, or rate.Sampling at a rate higher than the Nyquist rate is called oversampling. This is routinelyperformed where it is essential to recover a true replica of the signal being sampled. When asignal is sampled at less than the Nyquist rate, this is known as undersampling and can leadto erroneous results.To intuitively understand what happens when a signal is oversampled compared to a signalthat is sampled less than the Nyquist sampling rate, consider Figure 5.13.